2023 AMC 12A Problems/Problem 7
Problem
Janet rolls a standard 
-sided die 
times and keeps a running total of the numbers
she rolls. What is the probability that at some point, her running total will equal 
?
Solution 1
There are cases where her running total can equal :
1. She rolled 
for three times consecutively from the beginning. Probability: 
1
2
frac{1}{6^2} = frac{1}{36}
3. She rolled a 
, then . Probability: 
3
frac{1}{6}
Add them together to get 
